Oscillator and thermostat

TL;DR

This paper investigates how a finite-dimensional oscillator interacts with an infinite-dimensional thermostat, revealing that the thermostat induces effective dissipation in the oscillator despite energy conservation.

Contribution

It demonstrates that under natural assumptions, the complex Lagrangian system simplifies to effective dissipation in the finite-dimensional component due to the thermostat.

Findings

Thermostat induces effective dissipation in the oscillator.

Total system remains energy-preserving despite dissipation.

Finite-dimensional dynamics become simple over time.

Abstract

We study the problem of a potential interaction of a finite-dimensional Lagrangian system (an oscillator) with a linear infinite-dimensional one (a thermostat). In spite of the energy preservation and the Lagrangian (Hamiltonian) nature of the total system, under some natural assumptions the final dynamics of the finite-dimensional component turns out to be simple while the thermostat produces an effective dissipation.